I've commuted on a bike in winter for 13 years now, but never as far as now, that is 30 km daily. I have a problem which I never experienced before.
In temperatures close to 0C and on paths covered ...

There is a lot of snow in the winter where I live. Different kinds of snow; soft, sticky, wet, etc. And ice too. It can get pretty cold: -25 °C (-15 °F). We drop salt, sand and gravel on our roads.
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